Finite Group Databasebeta

?

← Prev (#44567202) Next (#44567204) →

C₃⋊(D₁₇₈₉⋊C₃) #44567203

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1792 points:

(2,3)(5,9,10,6,7,11)(8,17,18,12,13,27)(14,30,31,20,21,44)(15,29,25,23,19,16)(22,49,50,33,34,67)(24,47,48,36,32,41)(26,28,46,38,39,42)(35,72,73,52,53,96)(37,70,71,55,51,64)(40,45,69,57,58,65)(43,85,83,61,62,60)(54,101,102,75,76,131)(56,99,100,78,74,93)(59,68,98,80,81,94)(63,114,115,86,87,89)(66,120,112,90,91,84)(77,136,137,104,105,172)(79,134,135,107,103,128)(82,97,133,109,110,129)(88,149,150,116,117,124)(92,156,154,121,122,119)(95,161,147,125,126,113)(106,177,178,139,140,219)(108,175,176,142,138,169)(111,132,174,144,145,170)(118,190,191,151,152,165)(123,197,198,157,158,160)(127,203,195,162,163,155)(130,208,188,166,167,148)(141,224,225,180,181,272)(143,222,223,183,179,216)(146,173,221,185,186,217)(153,237,238,192,193,212)(159,244,245,199,200,207)(164,251,249,204,205,202)(168,256,242,209,210,196)(171,261,235,213,214,189)(182,277,278,227,228,331)(184,275,276,230,226,269)(187,220,274,232,233,270)(194,290,291,239,240,265)(201,297,298,246,247,260)(206,304,305,252,253,255)(211,310,302,257,258,250)(215,315,295,262,263,243)(218,320,288,266,267,236)(229,336,337,280,281,396)(231,334,335,283,279,328)(234,273,333,285,286,329)(241,349,350,292,293,324)(248,356,357,299,300,319)(254,363,364,306,307,314)(259,370,368,311,312,309)(264,375,361,316,317,303)(268,380,354,321,322,296)(271,385,347,325,326,289)(282,401,402,339,340,467)(284,399,400,342,338,393)(287,332,398,344,345,394)(294,414,415,351,352,389)(301,421,422,358,359,384)(308,428,429,365,366,379)(313,435,436,371,372,374)(318,441,433,376,377,369)(323,446,426,381,382,362)(327,451,419,386,387,355)(330,456,412,390,391,348)(341,472,473,404,405,544)(343,470,471,407,403,464)(346,397,469,409,410,465)(353,485,486,416,417,460)(360,492,493,423,424,455)(367,499,500,430,431,450)(373,506,507,437,438,445)(378,513,511,442,443,440)(383,518,504,447,448,434)(388,523,497,452,453,427)(392,528,490,457,458,420)(395,533,483,461,462,413)(406,549,550,475,476,627)(408,547,548,478,474,541)(411,468,546,480,481,542)(418,562,563,487,488,537)(425,569,570,494,495,532)(432,576,577,501,502,527)(439,583,584,508,509,522)(444,590,591,514,515,517)(449,596,588,519,520,512)(454,601,581,524,525,505)(459,606,574,529,530,498)(463,611,567,534,535,491)(466,616,560,538,539,484)(477,632,633,552,553,716)(479,630,631,555,551,624)(482,545,629,557,558,625)(489,645,646,564,565,620)(496,652,653,571,572,615)(503,659,660,578,579,610)(510,666,667,585,586,605)(516,673,674,592,593,600)(521,680,678,597,598,595)(526,685,671,602,603,589)(531,690,664,607,608,582)(536,695,657,612,613,575)(540,700,650,617,618,568)(543,705,643,621,622,561)(554,721,722,635,636,811)(556,719,720,638,634,713)(559,628,718,640,641,714)(566,734,735,647,648,709)(573,741,742,654,655,704)(580,748,749,661,662,699)(587,755,756,668,669,694)(594,762,763,675,676,689)(599,769,770,681,682,684)(604,775,767,686,687,679)(609,780,760,691,692,672)(614,785,753,696,697,665)(619,790,746,701,702,658)(623,795,739,706,707,651)(626,800,732,710,711,644)(637,816,817,724,725,912)(639,814,815,727,723,808)(642,717,813,729,730,809)(649,829,830,736,737,804)(656,836,837,743,744,799)(663,843,844,750,751,794)(670,850,851,757,758,789)(677,857,858,764,765,784)(683,864,865,771,772,779)(688,871,869,776,777,774)(693,876,862,781,782,768)(698,881,855,786,787,761)(703,886,848,791,792,754)(708,891,841,796,797,747)(712,896,834,801,802,740)(715,901,827,805,806,733)(726,917,918,819,820,1019)(728,915,916,822,818,909)(731,812,914,824,825,910)(738,930,931,831,832,905)(745,937,938,838,839,900)(752,944,945,845,846,895)(759,951,952,852,853,890)(766,958,959,859,860,885)(773,965,966,866,867,880)(778,972,973,872,873,875)(783,978,970,877,878,870)(788,983,963,882,883,863)(793,988,956,887,888,856)(798,993,949,892,893,849)(803,998,942,897,898,842)(807,1003,935,902,903,835)(810,1008,928,906,907,828)(821,1024,1025,920,921,1132)(823,1022,1023,923,919,1016)(826,913,1021,925,926,1017)(833,1037,1038,932,933,1012)(840,1044,1045,939,940,1007)(847,1051,1052,946,947,1002)(854,1058,1059,953,954,997)(861,1065,1066,960,961,992)(868,1072,1073,967,968,987)(874,1079,1080,974,975,982)(879,1086,1084,979,980,977)(884,1091,1077,984,985,971)(889,1096,1070,989,990,964)(894,1101,1063,994,995,957)(899,1106,1056,999,1000,950)(904,1111,1049,1004,1005,943)(908,1116,1042,1009,1010,936)(911,1121,1035,1013,1014,929)(922,1137,1138,1027,1028,1251)(924,1135,1136,1030,1026,1129)(927,1020,1134,1032,1033,1130)(934,1150,1151,1039,1040,1125)(941,1157,1158,1046,1047,1120)(948,1164,1165,1053,1054,1115)(955,1171,1172,1060,1061,1110)(962,1178,1179,1067,1068,1105)(969,1185,1186,1074,1075,1100)(976,1192,1193,1081,1082,1095)(981,1199,1200,1087,1088,1090)(986,1205,1197,1092,1093,1085)(991,1210,1190,1097,1098,1078)(996,1215,1183,1102,1103,1071)(1001,1220,1176,1107,1108,1064)(1006,1225,1169,1112,1113,1057)(1011,1230,1162,1117,1118,1050)(1015,1235,1155,1122,1123,1043)(1018,1240,1148,1126,1127,1036)(1029,1256,1257,1140,1141,1376)(1031,1254,1255,1143,1139,1248)(1034,1133,1253,1145,1146,1249)(1041,1269,1270,1152,1153,1244)(1048,1276,1277,1159,1160,1239)(1055,1283,1284,1166,1167,1234)(1062,1290,1291,1173,1174,1229)(1069,1297,1298,1180,1181,1224)(1076,1304,1305,1187,1188,1219)(1083,1311,1312,1194,1195,1214)(1089,1318,1319,1201,1202,1209)(1094,1325,1323,1206,1207,1204)(1099,1330,1316,1211,1212,1198)(1104,1335,1309,1216,1217,1191)(1109,1340,1302,1221,1222,1184)(1114,1345,1295,1226,1227,1177)(1119,1350,1288,1231,1232,1170)(1124,1355,1281,1236,1237,1163)(1128,1360,1274,1241,1242,1156)(1131,1365,1267,1245,1246,1149)(1142,1381,1382,1259,1260,1507)(1144,1379,1380,1262,1258,1373)(1147,1252,1378,1264,1265,1374)(1154,1394,1395,1271,1272,1369)(1161,1401,1402,1278,1279,1364)(1168,1408,1409,1285,1286,1359)(1175,1415,1416,1292,1293,1354)(1182,1422,1423,1299,1300,1349)(1189,1429,1430,1306,1307,1344)(1196,1436,1437,1313,1314,1339)(1203,1443,1444,1320,1321,1334)(1208,1450,1451,1326,1327,1329)(1213,1456,1448,1331,1332,1324)(1218,1461,1441,1336,1337,1317)(1223,1466,1434,1341,1342,1310)(1228,1471,1427,1346,1347,1303)(1233,1476,1420,1351,1352,1296)(1238,1481,1413,1356,1357,1289)(1243,1486,1406,1361,1362,1282)(1247,1491,1399,1366,1367,1275)(1250,1496,1392,1370,1371,1268)(1261,1512,1513,1384,1385,1630)(1263,1510,1511,1387,1383,1504)(1266,1377,1509,1389,1390,1505)(1273,1524,1525,1396,1397,1500)(1280,1531,1532,1403,1404,1495)(1287,1538,1539,1410,1411,1490)(1294,1545,1546,1417,1418,1485)(1301,1552,1553,1424,1425,1480)(1308,1559,1560,1431,1432,1475)(1315,1566,1567,1438,1439,1470)(1322,1573,1574,1445,1446,1465)(1328,1580,1516,1452,1453,1460)(1333,1586,1584,1457,1458,1455)(1338,1590,1578,1462,1463,1449)(1343,1594,1571,1467,1468,1442)(1348,1598,1564,1472,1473,1435)(1353,1603,1557,1477,1478,1428)(1358,1608,1550,1482,1483,1421)(1363,1613,1543,1487,1488,1414)(1368,1618,1536,1492,1493,1407)(1372,1621,1529,1497,1498,1400)(1375,1624,1522,1501,1502,1393)(1386,1587,1588,1515,1459,1689)(1388,1632,1633,1517,1514,1628)(1391,1508,1631,1519,1520,1629)(1398,1638,1639,1526,1527,1626)(1405,1645,1646,1533,1534,1623)(1412,1652,1653,1540,1541,1620)(1419,1659,1660,1547,1548,1617)(1426,1665,1666,1554,1555,1612)(1433,1670,1671,1561,1562,1607)(1440,1675,1676,1568,1569,1602)(1447,1680,1681,1575,1576,1597)(1454,1685,1635,1581,1582,1593)(1464,1692,1521,1591,1592,1585)(1469,1693,1637,1595,1596,1579)(1474,1695,1644,1599,1600,1572)(1479,1698,1651,1604,1605,1565)(1484,1701,1658,1609,1610,1558)(1489,1704,1664,1614,1615,1551)(1494,1705,1657,1616,1619,1544)(1499,1702,1650,1611,1622,1537)(1503,1699,1643,1606,1625,1530)(1506,1696,1636,1601,1627,1523)(1518,1690,1691,1634,1589,1711)(1528,1712,1713,1640,1641,1710)(1535,1714,1715,1647,1648,1709)(1542,1718,1719,1654,1655,1708)(1549,1723,1724,1661,1662,1707)(1556,1728,1729,1667,1668,1706)(1563,1733,1734,1672,1673,1703)(1570,1738,1739,1677,1678,1700)(1577,1743,1717,1682,1683,1697)(1583,1747,1642,1686,1687,1694)(1649,1748,1749,1716,1688,1756)(1656,1757,1758,1720,1721,1755)(1663,1759,1760,1725,1726,1754)(1669,1763,1764,1730,1731,1753)(1674,1768,1769,1735,1736,1752)(1679,1773,1762,1740,1741,1751)(1684,1777,1722,1744,1745,1750)(1727,1778,1779,1761,1746,1783)(1732,1784,1785,1765,1766,1782)(1737,1786,1787,1770,1771,1781)(1742,1789,1767,1774,1775,1780)(1772,1790,1791,1788,1776,1792);(1,2,3)(4,5,8,14,22,35,54,77,106,141,182,229,282,341,406,477,554,637,726,821,922,1029,1142,1261,1386,1516,1444,1312,1186,1066,952,844,742,646,548,402,469,533,528,523,518,513,506,499,492,485,470,401,468,543,623,708,798,894,996,1104,1218,1338,1464,1385,1514,1527,1534,1541,1548,1555,1562,1569,1576,1582,1588,1592,1596,1600,1605,1610,1615,1619,1622,1625,1627,1629,1630,1711,1747,1743,1738,1733,1728,1723,1718,1714,1712,1690,1587,1457,1331,1211,1097,989,887,791,701,617,538,410,281,338,352,359,366,372,377,382,387,391,394,396,464,537,615,699,789,885,987,1095,1209,1329,1455,1585,1519,1389,1264,1145,1032,925,824,729,640,557,480,409,344,285,232,185,144,109,80,57,38,25,10,9,15,24,37,56,79,108,143,184,231,284,343,408,479,556,639,728,823,924,1031,1144,1263,1388,1518,1635,1574,1437,1305,1179,1059,945,837,735,631,473,546,616,611,606,601,596,590,583,576,569,562,547,472,545,626,712,803,899,1001,1109,1223,1343,1469,1520,1260,1383,1397,1404,1411,1418,1425,1432,1439,1446,1453,1458,1463,1468,1473,1478,1483,1488,1493,1498,1502,1505,1507,1628,1710,1756,1777,1773,1768,1763,1759,1757,1748,1686,1581,1452,1326,1206,1092,984,882,786,696,612,534,461,345,228,279,293,300,307,312,317,322,326,329,331,393,460,532,610,694,784,880,982,1090,1204,1324,1449,1579,1636,1522,1392,1267,1148,1035,928,827,732,643,560,483,412,347,288,235,188,147,112,83,48,18,29,17,28,43,63,88,118,153,194,241,294,353,418,489,566,649,738,833,934,1041,1154,1273,1398,1528,1642,1681,1567,1430,1298,1172,1052,938,830,720,550,629,705,700,695,690,685,680,673,666,659,652,645,630,549,628,715,807,904,1006,1114,1228,1348,1474,1601,1390,1141,1258,1272,1279,1286,1293,1300,1307,1314,1321,1327,1332,1337,1342,1347,1352,1357,1362,1367,1371,1374,1376,1504,1626,1709,1755,1783,1789,1786,1784,1778,1744,1682,1575,1445,1320,1201,1087,979,877,781,691,607,529,457,390,286,181,226,240,247,253,258,263,267,270,272,328,389,455,527,605,689,779,875,977,1085,1198,1317,1442,1572,1643,1529,1399,1274,1155,1042,935,834,739,650,567,490,419,354,295,242,195,154,115,71,31,46,47,30,45,66,92,123,159,201,248,301,360,425,496,573,656,745,840,941,1048,1161,1280,1405,1535,1649,1717,1676,1560,1423,1291,1165,1045,931,815,633,718,800,795,790,785,780,775,769,762,755,748,741,734,719,632,717,810,908,1011,1119,1233,1353,1479,1606,1501,1265,1028,1139,1153,1160,1167,1174,1181,1188,1195,1202,1207,1212,1217,1222,1227,1232,1237,1242,1246,1249,1251,1373,1500,1623,1708,1754,1782,1792,1790,1774,1740,1677,1568,1438,1313,1194,1081,974,872,776,686,602,524,452,386,325,233,140,179,193,200,205,210,214,217,219,269,324,384,450,522,600,684,774,870,971,1078,1191,1310,1435,1565,1650,1536,1406,1281,1162,1049,942,841,746,657,574,497,426,361,302,249,198,150,100,50,69,85,70,49,68,95,127,164,206,254,308,367,432,503,580,663,752,847,948,1055,1168,1287,1412,1542,1656,1722,1739,1671,1553,1416,1284,1158,1038,916,722,813,901,896,891,886,881,876,871,864,857,850,843,836,829,814,721,812,911,1015,1124,1238,1358,1484,1611,1497,1370,1146,921,1026,1040,1047,1054,1061,1068,1075,1082,1088,1093,1098,1103,1108,1113,1118,1123,1127,1130,1132,1248,1369,1495,1620,1707,1753,1781,1788,1770,1735,1672,1561,1431,1306,1187,1074,967,866,771,681,597,519,447,381,321,266,186,105,138,152,158,163,167,170,172,216,265,319,379,445,517,595,679,768,863,964,1071,1184,1303,1428,1558,1657,1543,1413,1288,1169,1056,949,848,753,664,581,504,433,368,305,245,191,135,73,98,120,114,99,72,97,130,168,211,259,313,373,439,510,587,670,759,854,955,1062,1175,1294,1419,1549,1663,1727,1762,1734,1666,1546,1409,1277,1151,1023,817,914,1008,1003,998,993,988,983,978,972,965,958,951,944,937,930,915,816,913,1018,1128,1243,1363,1489,1616,1492,1366,1245,1033,820,919,933,940,947,954,961,968,975,980,985,990,995,1000,1005,1010,1014,1017,1019,1129,1244,1364,1490,1617,1706,1752,1780,1765,1730,1667,1554,1424,1299,1180,1067,960,859,764,675,592,514,442,376,316,262,213,145,76,103,117,122,126,129,131,169,212,260,314,374,440,512,589,672,761,856,957,1064,1177,1296,1421,1551,1664,1550,1420,1295,1176,1063,956,855,760,671,588,511,436,364,298,238,176,102,133,161,156,149,134,101,132,171,215,264,318,378,444,516,594,677,766,861,962,1069,1182,1301,1426,1556,1669,1732,1767,1769,1729,1660,1539,1402,1270,1136,918,1021,1121,1116,1111,1106,1101,1096,1091,1086,1079,1072,1065,1058,1051,1044,1037,1022,917,1020,1131,1247,1368,1494,1614,1487,1361,1241,1126,926,725,818,832,839,846,853,860,867,873,878,883,888,893,898,903,907,910,912,1016,1125,1239,1359,1485,1612,1703,1751,1761,1725,1661,1547,1417,1292,1173,1060,953,852,757,668,585,508,437,371,311,257,209,166,110,53,74,87,91,94,96,128,165,207,255,309,369,434,505,582,665,754,849,950,1057,1170,1289,1414,1544,1658,1557,1427,1302,1183,1070,963,862,767,678,591,507,429,357,291,223,137,174,208,203,197,190,175,136,173,218,268,323,383,449,521,599,683,773,868,969,1076,1189,1308,1433,1563,1674,1737,1772,1787,1764,1724,1653,1532,1395,1255,1025,1134,1240,1235,1230,1225,1220,1215,1210,1205,1199,1192,1185,1178,1171,1164,1157,1150,1135,1024,1133,1250,1372,1499,1609,1482,1356,1236,1122,1013,825,636,723,737,744,751,758,765,772,777,782,787,792,797,802,806,809,811,909,1012,1120,1234,1354,1480,1607,1700,1750,1720,1654,1540,1410,1285,1166,1053,946,845,750,661,578,501,430,365,306,252,204,162,125,81,34,51,62,65,67,93,124,160,202,250,303,362,427,498,575,658,747,842,943,1050,1163,1282,1407,1537,1651,1564,1434,1309,1190,1077,970,869,770,674,584,500,422,350,276,178,221,261,256,251,244,237,222,177,220,271,327,388,454,526,604,688,778,874,976,1083,1196,1315,1440,1570,1679,1742,1776,1791,1785,1760,1719,1646,1525,1380,1138,1253,1365,1360,1355,1350,1345,1340,1335,1330,1325,1318,1311,1304,1297,1290,1283,1276,1269,1254,1137,1252,1375,1503,1604,1477,1351,1231,1117,1009,906,730,553,634,648,655,662,669,676,682,687,692,697,702,707,711,714,716,808,905,1007,1115,1229,1349,1475,1602,1697,1716,1647,1533,1403,1278,1159,1046,939,838,743,654,571,494,423,358,299,246,199,157,121,90,58,21,32,42,44,64,89,119,155,196,243,296,355,420,491,568,651,740,835,936,1043,1156,1275,1400,1530,1644,1571,1441,1316,1197,1084,973,865,763,667,577,493,415,335,225,274,320,315,310,304,297,290,275,224,273,330,392,459,531,609,693,783,879,981,1089,1203,1322,1447,1577,1684,1746,1766,1771,1775,1779,1758,1715,1639,1511,1257,1378,1496,1491,1486,1481,1476,1471,1466,1461,1456,1450,1443,1436,1429,1422,1415,1408,1401,1394,1379,1256,1377,1506,1599,1472,1346,1226,1112,1004,902,805,641,476,551,565,572,579,586,593,598,603,608,613,618,622,625,627,713,804,900,1002,1110,1224,1344,1470,1597,1694,1640,1526,1396,1271,1152,1039,932,831,736,647,564,487,416,351,292,239,192,151,116,86,61,39,13,19,27,41,60,84,113,148,189,236,289,348,413,484,561,644,733,828,929,1036,1149,1268,1393,1523,1637,1578,1448,1323,1200,1080,966,858,756,660,570,486,400,278,333,385,380,375,370,363,356,349,334,277,332,395,463,536,614,698,788,884,986,1094,1208,1328,1454,1583,1688,1721,1726,1731,1736,1741,1745,1749,1713,1633,1382,1509,1624,1621,1618,1613,1608,1603,1598,1594,1590,1586,1580,1573,1566,1559,1552,1545,1538,1531,1524,1510,1381,1508,1595,1467,1341,1221,1107,999,897,801,710,558,405,474,488,495,502,509,515,520,525,530,535,539,542,544,624,709,799,895,997,1105,1219,1339,1465,1593,1634,1517,1387,1262,1143,1030,923,822,727,638,555,478,407,342,283,230,183,142,107,78,55,36,23,7,11,16,26,40,59,82,111,146,187,234,287,346,411,482,559,642,731,826,927,1034,1147,1266,1391,1521,1584,1451,1319,1193,1073,959,851,749,653,563,471,337,398,456,451,446,441,435,428,421,414,399,336,397,466,540,619,703,793,889,991,1099,1213,1333,1459,1589,1641,1648,1655,1662,1668,1673,1678,1683,1687,1691,1513,1631,1696,1699,1702,1705,1704,1701,1698,1695,1693,1692,1689,1685,1680,1675,1670,1665,1659,1652,1645,1638,1632,1512,1591,1462,1336,1216,1102,994,892,796,706,621,481,340,403,417,424,431,438,443,448,453,458,462,465,467,541,620,704,794,890,992,1100,1214,1334,1460,1515,1384,1259,1140,1027,920,819,724,635,552,475,404,339,280,227,180,139,104,75,52,33,20,12,6)

Polycyclic presentation:

2,3^2,1789|c^a=c^2,d^a=d^1788,d^b=d^1636

Conjugacy classes & character table

903 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32202, 9);